TPTP Problem File: SEV486^1.p

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% File     : SEV486^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : FINITE_NUMSEG_LT
% Version  : Especial.
% English  :

% Refs     : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source   : [Kal16]
% Names    : FINITE_NUMSEG_LT_.p [Kal16]

% Status   : Theorem
% Rating   : 0.00 v7.1.0
% Syntax   : Number of formulae    :   10 (   0 unit;   7 type;   0 defn)
%            Number of atoms       :   36 (   2 equality;  17 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :   29 (   0   ~;   0   |;   1   &;  28   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   14 (   0 sgn;   5   !;   2   ?;   2   ^)
%                                         (  14   :;   5  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

% Comments : Exported from core HOL Light.
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thf('thf_type_type/nums/num',type,(
    'type/nums/num': $tType )).

thf('thf_const_const/sets/SETSPEC',type,(
    'const/sets/SETSPEC': 
      !>[A: $tType] :
        ( A > $o > A > $o ) )).

thf('thf_const_const/sets/HAS_SIZE',type,(
    'const/sets/HAS_SIZE': 
      !>[A: $tType] :
        ( ( A > $o ) > 'type/nums/num' > $o ) )).

thf('thf_const_const/sets/GSPEC',type,(
    'const/sets/GSPEC': 
      !>[A: $tType] :
        ( ( A > $o ) > A > $o ) )).

thf('thf_const_const/sets/FINITE',type,(
    'const/sets/FINITE': 
      !>[A: $tType] :
        ( ( A > $o ) > $o ) )).

thf('thf_const_const/sets/CARD',type,(
    'const/sets/CARD': 
      !>[A: $tType] :
        ( ( A > $o ) > 'type/nums/num' ) )).

thf('thf_const_const/arith/<',type,(
    'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o )).

thf('thm/sets/HAS_SIZE_NUMSEG_LT_',axiom,(
    ! [A: 'type/nums/num'] :
      ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
      @ ( 'const/sets/GSPEC' @ 'type/nums/num'
        @ ^ [A0: 'type/nums/num'] :
          ? [A1: 'type/nums/num'] :
            ( 'const/sets/SETSPEC' @ 'type/nums/num' @ A0 @ ( 'const/arith/<' @ A1 @ A ) @ A1 ) )
      @ A ) )).

thf('thm/sets/HAS_SIZE_',axiom,(
    ! [A: $tType,A0: A > $o,A1: 'type/nums/num'] :
      ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A1 )
      = ( ( 'const/sets/FINITE' @ A @ A0 )
        & ( ( 'const/sets/CARD' @ A @ A0 )
          = A1 ) ) ) )).

thf('thm/sets/FINITE_NUMSEG_LT_',conjecture,(
    ! [A: 'type/nums/num'] :
      ( 'const/sets/FINITE' @ 'type/nums/num'
      @ ( 'const/sets/GSPEC' @ 'type/nums/num'
        @ ^ [A0: 'type/nums/num'] :
          ? [A1: 'type/nums/num'] :
            ( 'const/sets/SETSPEC' @ 'type/nums/num' @ A0 @ ( 'const/arith/<' @ A1 @ A ) @ A1 ) ) ) )).

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